Bios 776, HW # 9
Assigned: Mon, 30 Mar 2015
Due: Mon, 6 Apr 2015
1. Read 13 of HR.
2. Assess the eect of baseline smoking intensity A on weight change Y in
the NHEFS study by tting the MSM
E[Y a ] = 0 + 1 A + 2 A2 .
Describe how the model was t and justif

Bios 776, HW # 3
Assigned: 21 Jan 2015
Due: 28 Jan 2015
1. Conduct the following simple simulation study to demonstrate that the
standardized mean and IPW estimators from 2 of HR are empirically
unbiased in large samples. Stochastically generate a data se

Bios 776, HW # 2
Assigned: 14 Jan 2015
Due: 21 Jan 2015
1. Suppose we are willing to assume exchangeability (e.g., as in a randomize
experiment as in 2). Assume we observe n iid copies of (Y, A) which we
denote (Y1 , A1 ), . . . , (Yn , An ). Consider the

Bios 776, HW # 4
Assigned: Wed, 28 Jan 2015
Due: Wed, 4 Feb 2015
For problems 1 4, assume M , A, and Y are binary random variables as in 4
of HR.
1. (cf 4.1) Prove there is qualitative, additive eect modication if and only
if there is qualitative, multipl

Bios 776, HW # 7
Assigned: Mon, 23 Feb 2015
Due: Mon, 2 Mar 2015
1. Read 10 of HR.
2. Assume a completely randomized experiment where k of n individuals are
randomly assigned treatment. Prove the classic result due to Neyman (cf.
slide 13 on 10) that
Ecfw

Bios 776, HW # 5
Assigned: Wed, 4 Feb 2015
Due: Wed, 11 Feb 2015
Consider the following DAG
L1
W1
Z1
U1
X
L2
Y
W2
Z2
U2
L3
W3
Z3
Figure 1: See Question 2 and 3.
1. Which vertices are d-separated from Y if we do not condition on any
variables? Provide a ju

(b) Now suppose that we are given a joint distribution P (A, B, C, D, E)
that factorizes according to an unknown DAG G . Further suppose
that the following independence relations hold in the distribution
PBios 776, HW # 6 E)
(A, B, C, D,
Assigned: Wed, 11

Bios 776, HW # 8
Assigned: Mon, 23 Mar 2015
Due: Mon, 30 Mar 2015
1. Read 11 - 12 of HR.
2. Consider the estimators 0 and 1 which minimize
Wicfw_Yi (0 + 1Ai)2.
Prove
WiYi Ai WiYi (1 Ai )
1 =
.
Wi Ai
Wi (1 Ai )
3. On slide 15 of the class notes on 12 i

Bios 776, HW # 10
Assigned: Mon, 6 Apr 2015
Due: Mon, 13 Apr 2015
1. Read 14 15 of HR.
2. Conduct an analysis assessing the eect of smoking cessation (qsmk) A
on death Y in the NHEFS study by (i) tting a MSM via IPW, (ii) the
parametric G-formula, and (ii

Bios 776, HW # 1
Assigned: Wed, 7 Jan 2015
Due: Wed, 14 Jan 2015
1. Read 1 of Hernan and Robins (HR).
2. As in HR, let A denote treatment and Y a binary outcome where Y = 1
denotes death and Y = 0 denotes survival. Using the concept of potential outcomes,